Field
This disclosure relates to ophthalmic lenses used for both distance vision and near vision known as progressive addition lenses.
Description of the Related Art
Progressive addition lenses are configured in an attempt to allow a wearer to comfortably transition between lens powers within the lens in a smooth and seamless manner. To achieve this the configuration of progressive ophthalmic lenses typically uses the following merit function.
      Φ    0    =                    ∑                  i          =          1                N            ⁢                          ⁢                                    α            i                    ⁡                      (                                          C                i                            -                              C                                  0                  ⁢                                                                          ⁢                  i                                                      )                          2              +                  ∑                  i          =          1                N            ⁢                          ⁢                                    β            i                    ⁡                      (                                          A                i                            -                              A                                  0                  ⁢                                                                          ⁢                  i                                                      )                          2              +                  ∑                  i          =          1                N            ⁢                          ⁢                                    γ            i                    ⁡                      (                                          S                i                            -                              S                                  0                  ⁢                                                                          ⁢                  i                                                      )                          2              +                  ∑                  k          =          1                          M          c                    ⁢                          ⁢                        δ          k                ⁢                  C          k          2                      +                  ∑                  k          =          1                          M          c                    ⁢                                    ϵ            k                    ⁡                      (                                          S                k                            -                              S                                  0                  ⁢                                                                          ⁢                  k                                                      )                          2            In the merit function, i is an index which allows for evaluation of the possible sight directions to consider for the principal meridian of the progressive lens. For example, a grid of points regularly or irregularly scattered over the lens may be selected, and the gaze directions passing through each of these points may be evaluated. The index i traverses sight directions scattered or distributed over the lens. The index k traverses sight directions that pass through the principal meridian. In the merit function, C0i and A0i are the desired or optimal cylinder and cylinder axis at point i, whereas Ci and Ai are the cylinder and cylinder axis the lens actually has at the particular point i at a particular stage during optimization. Similarly, S0i is the desired or optimal sphere at point i, and Si is the sphere the lens actually has at this point at a particular stage during optimization. The variables αi,βi and γi are numbers used as weights that give different importance to different points. There are Nc sight directions going through the principal meridian of the progressive lens. These sight directions may be evenly distributed along the principal meridian, from the top to the bottom of the lens. The target astigmatism at the principal meridian is zero (in which case, there is no C0k), and the target sphere values at the principal meridian are S0k. The values Ck and Sk are the actual values of cylinder and sphere that the lens has at each point on the principal meridian. The variables δk and ∈k are weights used to optimize the cylinder and sphere along the principal meridian.
At multiple stages during optimization of a progressive lens design, the actual cylinder and sphere produced by the lens are calculated, and the value of the merit function Φ0 is computed. The theoretical surface of the lens is modified, and the merit function Φ0 is recomputed and compared with the previous value of the merit function for the previous point. This is reflected in the range i=1 through N in summations in the merit function. If the new value is smaller, the surface modifications are deemed acceptable. In this way, the merit function is evaluated through all points until the smallest possible value of the merit function Φ0 is achieved.
The prior paragraphs present a simplified description of the optimization process for progressive lens construction, and the actual process may differ considerably, though the final objective is the same: to produce a lens with distributions of C, A and S as similar as possible to the proposed objective distribution of C0,A0 and S0 over the entire lens, but especially on the principal meridian of the lens.
However, a problem with the traditional merit function used in progressive addition lens design is that the power components S, C and A are not independent of one another. These power components cannot be distributed independently over the lens surface. In practice, the resulting distributions of C0, A0 and S0 are not correctly established on the lens such that the optimization of the merit function yields less than optimal and sometimes incorrect results. This causes progressive lenses to be less than optimal and sometimes unsatisfactory to the lens wearing consumer.